Theory of Quantum Computation

Mingsheng Ying

Anas N. Rabadi

This paper introduces the new concept of Reversible Game Theory (RGT) and its Multiple-Valued Quantum Computation (MVQC). Game Theory (GT) involves the study of competition and cooperation, without regard to the particular entities (agents) involved, and issues of rationality associated with such phenomena. Reversibility property in GT can be important in situations where: (1) an outside observer needs to know reversely the paths that lead to specific payoffs on a game’s extensive form, and (2) modeling the (maximin) dynamics using low-power consuming circuits as reversibility is a main requirement for low-power circuit design of future technologies such as in Quantum Computing (QC). Quantum Decision Trees (QDTs) are also presented as a quantum representation for applying MVQC to games’ dynamics.

Vijey Thayananthan

In this paper, we describe the trellis coding where quantum computing (QC) is employed to analyze the coding gain and complexity.According to quantum information theory, quantum bits increase the storage capacity as well as speed.High complex trellis based on partial memory code (PUM) is designed and simulated in digital computers.In order to reduce simulation time for trellis decoding, QC is analyzed with PUM coding.From the theoretical analysis, QC in a quantum computer will be the best option because quantum bits can be stored simultaneously in a given moment of time.From this theory, trellis states, paths, metric calculations are stored in lesser time and space than conventional storing procedures.Therefore, QC certainly will improve the trellis coder performance.

David Deutsch, ARTUR K. EKERT, Richard Jozsa +3 more

Xijia Miao

A unitary dynamical state-locking (UNIDYSLOCK) process is a unitary process that can transform two orthogonal states to two non-orthogonal states. Its inverse process, i.e., the QUANSDAM process could realize an exponential QC speedup in solving an unstructured search problem in the quantum-computing (QC) speedup theory (X. Miao, arXiv:1105.3573 [quant-ph] (2011)). In this paper the principle of how a UNIDYSLOCK process works is described on the basis of the QC speedup theory. A UNIDYSLOCK process does not exist at all in pure quantum mechanics. That it can change the quantum-state difference is original from the fundamental interaction between the quantum physical laws (i.e., the unitary quantum dynamics and the Hilbert-space symmetric structure) and the mathematical-logical principle of the search problem. It is characteristic for the QC speedup theory. Even if a usual quantum computational (Qc) process that is reversible or unitary contained a UNIDYSLOCK (or QUANSDAM) process, the contribution of the UNIDYSLOCK (or QUANSDAM) process to the QC speedup of the usual Qc process would be secondary or negligible. Whether or not a UNIDYSLOCK (or QUANSDAM) process can make an essential contribution to a QC speedup can distinguish the QC speedup theory from any usual Qc theory. In the paper the QC speedup mechanism of the HSSS quantum search process is also studied. The search process is essentially different from a usual quantum search algorithm. It works in both the usual Hilbert space and the math Hilbert space. Due to the math Hilbert space a mathematical-parallel operation is characteristic for the QC speedup theory, while a quantum-parallel operation is characteristic for the usual Qc theory. The fundamental interaction mentioned above and the fundamental quantum-computing resource play the main role in speeding up the search process.